On the formulations of higher-order strain gradient crystal plasticity models

Kuroda, Mitsutoshi; Tvergaard, Viggo

doi:10.1016/j.jmps.2007.07.015

Cited by 137 publications

(77 citation statements)

References 35 publications

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“…For a detailed discussion on the micro-structural boundary conditions see Kuroda and Tvergaard (2008).…”

Section: (α)mentioning

confidence: 99%

“…The results are obtained using the finite element method (FEM), solving the conventional system of equations and the GND system of equations in a staggered scheme. The discretized finite element equations can be found in Kuroda and Tvergaard (2008). Eight-node isoparametric quadrilateral elements with reduced Gauss integration are used for the displacement field analysis, whereas equivalent four-node elements with full Gauss integration are used for the GND density field analysis.…”

Section: Problem Descriptionmentioning

confidence: 99%

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On modeling micro-structural evolution using a higher order strain gradient continuum theory

El-Naaman

Nielsen

Niordson

2016

International Journal of Plasticity

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Published experimental measurements on deformed metal crystals show distinct pattern formation, in which dislocations are arranged in wall and cell structures. The distribution of dislocations is highly non-uniform, which produces discontinuities in the lattice rotations. Modeling the experimentally observed micro-structural behavior, within a framework based on continuous field quantities, poses obvious challenges, since the evolution of dislocation structures is inherently a discrete and discontinuous process. This challenge, in particular, motivates the present study, and the aim is to improve the micro-structural response predicted using strain gradient crystal plasticity within a continuum mechanics framework. One approach to modeling the dislocation structures observed is through a back stress formulation, which can be related directly to the strain gradient energy. The present work offers an investigation of constitutive equations for the back stress based on both considerations of the gradient energy, but also includes results obtained from a purely phenomenological starting point. The influence of model parameters is brought out in a parametric study, and it is demonstrated how a proper treatment of the back stress enables dislocation wall and cell structure * Tel: +45 4525-4020, Fax: +45 4593-1475 URL: saeln@mek.dtu.dk (S.A. El-Naaman)

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“…For a detailed discussion on the micro-structural boundary conditions see Kuroda and Tvergaard (2008).…”

Section: (α)mentioning

confidence: 99%

Section: Problem Descriptionmentioning

confidence: 99%

On modeling micro-structural evolution using a higher order strain gradient continuum theory

El-Naaman

Nielsen

Niordson

2016

International Journal of Plasticity

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“…Note that another class of theories, as developed for instance by Evers et al (2004) and Geers et al (2007), introduce the effect of the impenetrable boundaries by adding in the formulation a back stress related to the plastic incompatibility. Kuroda and Tvergaard (2008) have recently shown that this last class of non work conjugate theories is, under some assumptions, similar mathematically to the higher order conjugate theories of the class developed by Fleck and Hutchinson in the case of a crystal plasticity formulation.…”

Section: A C C E P T E D Article In Pressmentioning

confidence: 52%

Analysis of size effects associated to the transformation strain in TRIP steels with strain gradient plasticity

Mazzoni-Leduc

Pardoen

Massart

2010

European Journal of Mechanics - A/Solids

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International audienceThe size dependent strenghtening resulting from the transformation strain in Transformation Induced Plasticity (TRIP) steels is investigated using a two dimensional embedded cell model of a simplified microstructure composed of small cylindrical metastable austenitic inclusions within a ferritic matrix. Earlier studies have shown that within the framework of classical plasticity or of the single length parameter Fleck-Hutchinson strain gradient plasticity theory, the transformation strain has no significant impact on the overall strengthening. The strengthening is essentially coming from the composite effect with a marked inclusion size effect resulting from the appearance during deformation of new boundaries constraining the plastic flow. The three parameters version of the Fleck-Hutchinson strain gradient plasticity theory is used here in order to better capture the effect of the plastic strain gradients resulting from the transformation strain. The three parameters theory incorporates separately the rotational and extensional gradients in the formulation, which leads to a significant influence of the shear component of the transformation strain, not captured by the single parameter theory. When the size of the austenitic inclusions decreases, the overall strengthening increases due to a combined size dependent effect of the transformation strain and of the evolving composite structure. A parametric study is proposed and discussed in the light of experimental evidences giving indications on the optimization of the microstructure of TRIP-assisted multiphase steels

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“…Van Beers et al (2013) define the geometrically-motivated grain-boundary normal slip components (see Ertürk et al, 2009;Kuroda and Tvergaard, 2008) by…”

Section: Comparison Of Aspects Of the Gurtin And Van Beers Et Al Modelsmentioning

confidence: 99%

Computational and theoretical aspects of a grain-boundary model that accounts for grain misorientation and grain-boundary orientation

Gottschalk

McBride

Reddy

et al. 2016

Computational Materials Science

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A detailed theoretical and numerical investigation of the infinitesimal single-crystal gradientplasticity and grain-boundary theory of Gurtin (2008) "A theory of grain boundaries that accounts automatically for grain misorientation and grain-boundary orientation". Journal of the Mechanics and Physics of Solids 56 (2), 640-662, is performed. The governing equations and flow laws are recast in variational form. The associated incremental problem is formulated in minimization form and provides the basis for the subsequent finite element formulation. Various choices of the kinematic measure used to characterize the ability of the grain boundary to impede the flow of dislocations are compared. An alternative measure is also suggested. A series of threedimensional numerical examples serve to elucidate the theory.

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On the formulations of higher-order strain gradient crystal plasticity models

Cited by 137 publications

References 35 publications

On modeling micro-structural evolution using a higher order strain gradient continuum theory

On modeling micro-structural evolution using a higher order strain gradient continuum theory

Analysis of size effects associated to the transformation strain in TRIP steels with strain gradient plasticity

Computational and theoretical aspects of a grain-boundary model that accounts for grain misorientation and grain-boundary orientation

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